Non-standard bone simulations: Verification and validation

Standard methods for predicting bone’s mechanical response from quantitative computer-tomography(qCT) scans are mainly based on classical h-version Finite Element Methods (FEMs). This approach is often limited in terms of numerical accuracy and efficiency due to the low order polynomial approximation model, the need for segmentation, and the use of piecewise constant material properties assignment. Herein a non-standard method, the Finite Cell Method (FCM), is proposed for predicting the mechanical response of the human femur. The FCM is free of the above limitations associated with h-FEMs and is orders of magnitude more efficient, allowing its use in the setting of computational steering. This non-standard method applies a fictitious domain approach to simplify the modeling of a complex bone geometry obtained directly from Martin Ruess · Ernst Rank Chair for Computation in Engineering, Technische Universität München, Munich, Germany Tel.: +49-89-289-22425/-23047 Fax: +49-89-289-25051 E-mail: [email protected] / [email protected] David Tal · Nir Trabelsi Department of Mechanical Engineering, BenGurion-University of the Negev, Beer Sheva, Israel Tel: +972-8-647-7025 E-mail: [email protected] / [email protected] Zohar Yosibash Department of Mechanical Engineering, BenGurion-University of the Negev, Beer Sheva, Israel Tel: +972-8-647-7103 E-mail: [email protected] (Research performed while on Sabbatical leave at the Chair for Computation in Engineering at the Technische Universität München) a qCT scan, and takes into consideration easily the heterogeneous material distribution of the various bone regions of the femur. The fundamental principles and properties of the FCM are briefly described in relation to bone analysis, providing a theoretical basis for the comparison with the p-FEM as a reference analysis and simulation method of high quality. Both, p-FEM and FCM results are validated by comparison to an in-vitro experiment on a fresh-frozen femur.